Wow Ev, those are great observations you have there!
I was just involved in a recital, turns out that the recitalist and her other accompanist and I were all homeschooled. The other accompanist and I took turns singing duets with the recitalist. The recitalist is in public high school now, but she's the valedictorian - go figure! Homeschooling gave us all the time to develop our talent (and intellect).
Extracurricular activities are an excellent way to socialize, but the other important aspect of socialization is within the family. Spending time together and enjoying each other's company. It seems that school all too often pulls families apart, rather than together.